Holography

ABSTRACT

An iterative algorithm for hologram design with multiple output image planes arranged in close proximity to create continuous patterns within an imaging volume is disclosed. These may then be used for photolithography on 3D surfaces, or for generation of holograms for use in consumer devices.

TECHNICAL FIELD

The present invention relates to improvements in or relating to holography, and in particular to methods for generating holograms, together with associated apparatus for carrying out those methods. The improvements of this disclosure are applicable to holography for any purpose, for example, but without limitation, to the sphere of manufacturing processes such as photolithography, or to the sphere of consumer electronics products, such as holographic television or other devices.

BACKGROUND

As an example only, we discuss the field of lithography. Standard lithographic procedures, such as proximity and projection exposure, do not work well for non-planar substrates. Any conventional imaging system is limited by the depth of its point spread function. The image will become blurred or distorted away from its focal plane, leading to variation in feature width or to insufficient energy density for a well defined photoresist exposure.

Instead of a standard photomask, computer generated holograms (CGH) have been used to create focused patterns on 3D substrates [1, 2]. This method has hitherto been limited to the imaging of simple sparse line patterns. For more complex or dense patterns, mask implementation can become a problem as simultaneous modulation of amplitude and phase may be required.

It is known to employ wave-optics for enhanced photo-lithography. Simple serifs in lithography are applied to dampen the effects of diffraction. Also, fully diffraction simulated or analytical solutions have been investigated for planar and non-planar systems [11, 5, 2]. In planar systems, little advantage over existing proximity/contact techniques have been found but for non-planar substrates, diffractive masks have an advantage over simple proximity masks because patterns imaged over such substrates imaged by conventional means are severely degraded by diffraction effects. In contrast, properly implemented diffractive masks are capable of focusing patterns over a variable depth surface with relative ease.

There are existing methods for designing diffractive masks for photolithography over non-planar substrates: in the field of photolithography, superimposed holographic analytical line solutions have been utilised as a useful exposure technique for grossly non-planar substrates down to 5 -10 μm feature size[1] or over a depth of up to several cm [14] (see also [12]).

Such solutions however are not without problems. The simple numerical propagation and analytical solutions used to generate useable CGH patterns often require both phase and amplitude modulation which can be difficult and time consuming to fabricate; quantised amplitude-only reconstructions exhibit limited diffraction efficiency and tend to lead to low image fidelity and phase-only analytical approaches suffer from serious limitations in the geometry and density of line patterns

Iterative techniques are more suitable for maximising diffraction efficiency and have been used to generate diffractive optical masks for arbitrary intensity patterns over planar substrates. Iterative optimisation procedures based on the Gerchberg-Saxton (GS) algorithm [3] allow for a more general pattern geometry to be generated whilst maintaining a phase only CGH. However, holograms generated in this way will tend to produce large noise components in the reconstructed image, resulting in poor photoresist exposures. Others have overcome this by time averaging using an active modulation device [4] or have applied more complex systems and modeling techniques [5]. However, these methods are applied to planar substrates only. Accordingly, there is still a need for improvement with respect to 3D holography.

SUMMARY OF THE INVENTION

According to a first aspect of the present disclosure, there is provided a method of generating a wave-optical exposure mask comprising:

-   -   modifying the exposure mask via an iterative process until a         modulation pattern produced by the exposure mask produces a         desired non-planar pattern in object space; wherein     -   said iterative process comprises specifying an intensity pattern         that is defined over a bounded three dimensional geometrical         surface by a series of multiple planes provided at differing         positions within an image volume, extending from a diffraction         plane formed by the modulation; and     -   said iterative process is confined to a defined discrete array         of amplitude and/or phase altering elements.

The multiple planes may be planes which are cross-sectional (x,y) with respect to, and provided at different positions along, an optical axis, z, extending from the diffraction plane.

Optionally, said iterative process includes:

-   -   a long propagation from a diffraction plane (where the         modulation occurs) to a first endpoint of the object space where         the pattern is to be produced;     -   one or more short propagations traversing the object space while         applying different amplitude constraints across successive         planes;     -   a second long propagation from a second endpoint of the object         space where the pattern is to be produced back to the         diffraction plane; and     -   the application of a phase-only constraint in the diffraction         plane.

Optionally, the iterative process further includes filtering and spatial constraints applied at the diffraction plane.

Optionally, amplitude correction is applied to only a sub-portion of each image plane where the sampled pixels intersect a pseudo-continuous surface function.

Optionally, amplitude and phase information is unconstrained in unimportant selected areas of an image volume such as to allow the convergence of the algorithm. The amplitude and phase information may also be discarded where it is known that the surface prevents propagation.

Optionally, a propagation routine adopted to move between image planes and hologram is that of a convolution form of the Fresnel diffraction integral.

Alternatively, said propagation routine is an application of a Rayleigh-Somerfield propagator.

Alternatively, said propagation routine is an angular spectrum method.

Optionally, each image plane is corrected with an ideal amplitude profile, whilst retaining the propagated phase.

Optionally, the hologram plane itself is corrected with unit amplitude to give a phase only pattern.

According to a second aspect of the present disclosure, there is provided a wave-optical method of generating a hologram comprising:

-   -   providing coherent or partially coherent radiation;     -   modulating said incident radiation according to a modulation         pattern; and     -   varying said modulation pattern via an iterative process until         said modulation pattern produces a desired non-planar pattern in         object space;     -   wherein said iterative process comprises specifying an intensity         pattern     -    that is defined over a bounded three dimensional geometrical         surface by a series of multiple planes provided at differing         positions within an image volume, extending from a diffraction         plane formed by the modulation; and     -   said iterative process is confined to a defined discrete array         of amplitude and/or phase altering elements.

Steps forming optional parts of the first aspect as described above may be applied also to the method of the second aspect.

According to a third aspect of the present disclosure, there is provided an apparatus for generating a hologram having a desired non-planar pattern in object space, comprising:

-   -   a radiation source for emitting coherent or partially coherent         radiation;     -   a modulator for modulating said incident radiation according to         a modulation pattern;     -   said modulator being controllable to vary a pattern of         modulation that is applied; said apparatus comprising a         controller adapted to vary said modulation pattern via an         iterative process until said modulation pattern produces a         desired non-planar pattern in object space;     -   wherein said iterative process comprises specifying an intensity         pattern     -    that is defined over a bounded three dimensional geometrical         surface by a series of multiple planes provided at differing         positions within an image volume, extending from a diffraction         plane formed by the modulation; and said iterative process is         confined to a defined discrete array of amplitude and/or phase         altering elements.

Optionally, said modulator comprises a spatial light modulator (SLM).

Optionally, said radiation source comprises a laser.

According to a fourth aspect of the invention, there is provided a lithographic apparatus comprising the apparatus of the third aspect and arranged for carrying out the method of the first and/or the second aspect.

According to a fifth aspect of the invention, there is provided a consumer device for generating holograms which includes the apparatus of the third aspect and/or is arranged for carrying out the method of the first and/or second aspects.

Optionally, said consumer device comprises a holographic television with suitable projection means for projecting a hologram according to said predefined pattern into a viewing space or a display to be viewed by a user.

According to a sixth aspect of the present invention, there is provided a computer program product including instructions that, when run on an computer, enables said computer to implement the method of the first or second aspects, or to form part of the apparatus of the third, fourth or fifth aspects.

BRIEF DESCRIPTION OF THE DRAWINGS

The present invention will now be described, by way of example only, with reference to the accompanying drawings, in which:

FIG. 1 is a graphical illustration of a multi-plane algorithm according to an embodiment of the disclosure;

FIG. 2 illustrates a method of partial reinforcement, where amplitude correction is applied to only a sub-section of each image plane where the sampled pixels intersect the pseudo-continuous surface function;

FIG. 3 illustrates multiple plane constraints shown for an image volume divided into three planes;

FIG. 4 illustrates example average intensity profiles and center cross sections for a simulated non-planar surface. In FIG. 4( a) (the two left-hand side graphs), N=4 (δz=1365 μm), and in FIG. 4( b) (the two right-hand side graphs), N=20 (δz=215 μm);

FIG. 5 shows simulated contrast for variable plane separation (δz plotted on a log scale);

FIG. 6 illustrates an optical setup according to the present disclosure; and

FIG. 7 shows images of patterns developed on a coated substrate; with FIG. 7( a) illustrating a photoresist pattern on a flat top surface and FIG. 7( b) illustrating a photoresist pattern on a 45° sloped surface.

DETAILED DESCRIPTION

The present disclosure relates to a method of generating a wave-optical exposure mask that confines an incident coherent or partially-coherent wave according to a specified non-planar intensity pattern. A partial, multi-plane reinforcement method is disclosed that enables convergence to a suitable exposure mask with minimal error. The method consists of an optical design means that is subject to two fundamental constraints: Firstly, the specified intensity pattern is defined over a bounded three dimensional geometrical surface of the mathematical form z=f (x,y) by a series of multiple cross-sectional planes. Secondly, the exposure mask is intentionally confined to a defined discrete array of amplitude and/or phase altering elements to yield a diffractive optical mask.

The Gerchberg-Saxton [3] iterative phase reconstruction algorithm comprises a simple sequence which, when repeated, can converge to a hologram phase pattern given a pair of intensity conditions for hologram and image planes. Many variations and derivations of this algorithm have been applied to optics problems and, importantly, for both paraxial optical and far-field problems for which rapid algorithms such as the Fast Fourier transform (FFT) and the convolution form of the Fresnel diffraction equation may be implemented.

Generalisation of this approach beyond single image planes into a multiple output image planes which are propagated between in each iteration leads to methods for wave-optical mask design constrained to patterns on three dimensional planes. This in turn generates a quantised diffractive optical element which produces images at multiple depths.

In this method, restrictions are imposed across the entirety of every image plane in succession, by means of optical propagation between each neighbouring image plane. This computationally heavy approach has been successfully applied when the spacing between the multiple image planes is large in comparison to the general offset distance (defined as the distance between the diffractive element and the iteration plane nearest to the diffraction element (distance Z2 in FIG. 1).

The inventors have found that an iterative algorithm based on the Fresnel or angular-spectrum transformation can converge to holograms of continuous patterns for “thin” (on the order of the width of the point spread function) binary images. These are suitable for patterning of integrated circuit interconnections in a lithographic exposure. These methods are usually applied to a single planar image. To extend this method to 3D surfaces we have investigated multi-plane algorithms that are similar to those discussed in [6-8, 13] for display and optical tweezers applications, and have extended the constraints such that it becomes possible to form a continuous exposure pattern.

FIG. 1 shows a multi-plane algorithm illustrated graphically. An image volume of depth z₂ is divided into N image planes separated by a distance δz (δz=z₂/(N−1)). The image volume is offset from the diffraction plane hologram by a distance z₃. The distance from the diffraction plane to the furthest image plane is therefore z₁ (z₁=z₂+z₃).

Rather than a single output plane image, the algorithm invokes a numerically evaluated angular-spectrum propagation [9] between uniformly spaced planes inside an image volume and a single input diffraction plane. The process may be outlined as:

-   -   (I) a long forward propagation from the hologram to the furthest         plane in the image volume;     -   (II) short reverse propagation steps traversing the image volume         in conjunction with applying different amplitude constraints         across N planes separated by distance δz;     -   (III) a long reverse propagation from the image volume to the         diffraction plane;     -   (IV) a phase-only constraint applied in the diffraction plane in         which it is ensured that the total field energy remains         constant.

In step (IV), altering and spatial constraints may also be applied. As with the GS algorithm, the above process is repeated, and we expect the error to reduce in both the hologram and image.

Breaking the longer propagation transforms (I,III) into multiple steps allows the image to be calculated without incurring noise which would be caused by aliasing of the transfer function [10].

Separate amplitude constraints are applied on each image plane as shown by our test geometry in FIG. 3, which illustrates multiple plane constraints shown for a sparse case for N=3 i.e. where the image volume is divided into three planes. Surface patterns are then applied on the nearest constraint plane (along the optical axis).

To enable the algorithm to converge to a useful solution the image volume must not be over-constrained. A simple approach is therefore to constrain only those areas on each plane that intersect with the target surface. We also ensure that the pattern contains no constrained area that is directly occluded by another along the optical axis. This was shown to be able to produce relatively sparse image zones in [7], however we constrain ourselves to a real surface and endeavor to show experimentally that a continuous pattern can be generated onto photoresist, i.e. under constraints that are much tighter than those required for display applications. Within the constraint process, “high” regions are given field amplitude value 1 and low regions are set to 0.1 whilst phase is unchanged. Unconstrained areas remain unchanged in phase or amplitude. As discussed in [8], low regions cannot be set to zero as this would lead to a loss of phase information between propagation steps. The high/low ratio was chosen such as to enforce as large a contrast as possible without over-constraining the requirements on the image field.

The choice of “seeding” hologram to initialize the algorithm will influence the structure of the resulting pattern. A random phase distribution is often used but we have observed more reliable quality and faster convergence when applying an analytically derived initial hologram. Line segment holograms [2] can be used to generate image lines. To generate the initial hologram, we superimpose planar line segment holograms and then confine the resulting pattern to a phase-only distribution. This produces a non-ideal starting hologram, which is refined by the iterative procedure. Mathematically this approximation takes the form

$\begin{matrix} {U = {\left\{ {\sum\limits_{m = 1}^{M}\; \left\lbrack {\exp \left( \frac{{- {\pi}}\; d^{2}}{\lambda \left( {z_{3} + {z_{2}/2}} \right)} \right)} \right\rbrack} \right\} \times {{rect}\left( {\frac{x}{A},\frac{y}{B}} \right)}}} & (1) \end{matrix}$

where d=(y−pm−s) and y is the y direction coordinate of the hologram, p is the pitch of the lines to be imaged, s is an offset for alignment, M is the number of lines, and U is the hologram pattern. λ is the nominal wavelength of the illumination source. The 2D “rect” function limits the size of the hologram according to A and B where these are determined by the length of the lines and the width of the hologram respectively. A final further step is performed to curtail this to a phase only pattern.

When the plane separation is not large in comparison to the general offset distance it becomes difficult to constrain the problem because of the restriction that every pixel is constrained according to the desired image for every image plane. This becomes overly strict when it is considered that the image pattern need only be reinforced at the locations at which certain pixels intersect the surface function z=f (x,y). For most practical situations this leads to a greatly reduced degree of overall constraint to be applied in each image plane.

Taking the standard Gerchberg-Saxton routine, modification to add multiple planes [7,8] requires that, before propagating to the hologram plane, multiple planes in the image volume are successively calculated by short propagations between each plane, starting with the furthest, again as shown in FIG. 1. Each image plane is corrected with a ideal amplitude profile, whilst retaining propagated phase, thus reinforcing multiple images at separate depths along the optical axis. The hologram plane itself is corrected with unit amplitude to give a phase-only pattern.

For non-planar photo-lithography and other high fidelity 3D patterns this method becomes inadequate when planes with different values enforced in the same x-y coordinate area are pushed close together. This conflicting reinforcement stifles the ability of the algorithm to achieve sufficient contrast between a high intensity pixel in one image plane and low intensity pixel in the corresponding pixel of a neighbouring image plane. This presents an impractical constraint on the diffractive mask for larger patterns imaged over pseudo-continuous three dimensional surfaces.

The method of partial reinforcement proceeds by amplitude correction of only a sub-section of each image plane where the sampled pixels intersect the pseudo-continuous surface function, as shown in FIG. 2. Since we are only interested in the part of the volume which intersects with the surface of a photoresist coated substrate, we can break up our pattern into many planar sections rather than full planes. This type of technique has been seen to work in other publications [7] but under a much larger plane gap and not for a pseudo-continuous 3D pattern. We have advanced on this method by implementation of this technique on a real SLM device and with it have considered the physical sampling constraints involved in the system as well as taking the number of planes and plane gap to extremes with 256 planes spaced 4-40 μm apart.

As an example, a propagation routine adopted to move between image planes and the hologram is that of a convolution form of the Fresnel diffraction integral [9,10].

$\begin{matrix} {\mspace{79mu} {{{V\left( {x,y} \right)} = {\int{\int{{U\left( {\xi,\eta} \right)}{h\left( {{x - \xi},{y - \eta}} \right)}{\xi}{\eta}}}}}\mspace{79mu} {{h\left( {x,y} \right)} = \text{?}}{\text{?}\text{indicates text missing or illegible when filed}}}} & (1) \end{matrix}$

And |U(ξ, η) is the hologram plane field, V(x,y) is output plane field, z is distance along the optical axis, λ is wavelength and k=2π/λ. This convolution, evaluated numerically by applying a forward and inverse fast Fourier transform, leads to a relatively efficient calculation which retains 1:1 sample spacing on all input and output planes.

This propagation routine implemented numerically is immediately appropriate because of the retention of sample spacings and the validity of the propagation under short distances. Other routines however are just as viable, the angular spectrum method which retains the same advantages but has potential to propagate through rotation, this would mean that certain piecewise planar surfaces can be calculated with much greater efficiency. Another approach is application of Rayleigh-Somerfield propagator which at the expense of computation time increases the flexibility of the approach even further.

With any convolution based transformation (Fresnel, Angular-Spectrum and

some arrangements of Rayleigh-Sommerfeld), when evaluated numerically, the transfer function (TF) may be calculated in the frequency domain. This avoids un-necessary FFT operations. Expressed mathematically with the angular spectrum TF considered we have:

V(x,y)=

⁻¹(

(U(ξ,η)×H(v _(x) , v _(y)))

where

H(v _(x) ,v _(y))=e ^(j2πz)√{square root over ((1/λ)² +v _(x) ²³ +v _(y) ²)}

Where F is the Fourier transform (which would be evaluated using an FFT) and v_(x) and v_(y) are coordinates in the spatial frequency domain.

Adding still further to the completeness of the model, another constraint can be applied to planes within sections where our surface to be imaged upon is occluded by its geometry. As such we discard all amplitude and phase information where we know that the surface prevents propagation thus moving away from a completely free volume propagations into one that takes into account obstacles and occlusions.

Some implementations would constrain the iteration propagations to the sample spacings of the implementation medium, i.e. pixel pitch on the Liquid Crystal On Silicon (LcoS) Spatial Light Modulator or phase-only optic. This is improved by a routine which samples at above the implemented device pitch and imposes an sampling constraint at the hologram plane.

Combining these modifications to this multiple-plane iteration together with a set of depth masks and an array of closely spaced planes to propagate between therefore allows the algorithm to converge for different types of three dimensional surface geometries.

We turn now to discuss some examples of how these techniques can be applied. These examples are not limiting to the scope of the invention.

Running simulations with a sample pitch of 4 μm in both x & y and an image size of 8.192 mm×8.192 mm, we produce an image of a bus comprising 8 lines which descend a 45° slope and a total depth of z₂=4.096 mm, as shown in FIG. 3. The lines have a width of 8 μm at a pitch of 24 μm. The image volume is located at a distance of z₃=16 cm from the diffractive screen. For laser wavelength λ=405 nm, we have simulated a zone-plate point intensity profile image along the optical axis. A “full width at half maximum” measurement of this profile gives a depth of focus (DOF) of approximately 0.92 mm. Considering the depth of the surface topology this DOF would present a significant barrier to generating an focused image using a planar imaging system based on either refractive or holographic optical principals.

A set of holograms was generated, each by 50 iterations, using varying N (and subsequently δz). Example image line profiles and cross sections can be seen in FIG. 4. Dips in these profiles occur at the edge of each constrained region and are due to a combination of out of focus image patterns as the sloped surface is descended, and interference between the patterns imposed on separate planes.

Images generated were assessed according to the contrast parameter C=(H−L)/(H+L) [11] shown in FIG. 5. We choose L as the maximum background noise intensity value (i.e. in the “low” constrained regions, calculated from profiles taken between the image lines) and H as the minimum intensity value along simulated profiles of the lines (i.e. along the “high” constrained regions). This stringent measurement is calculated over the intended focal surface for an up-sampled hologram at increased resolution after the iterative procedure. This provides a comparison of pattern continuity as a higher contrast will result in a better defined exposed image area, making the exposure steps less sensitive to error.

Fluctuations present in the graph demonstrate high sensitivity to the local defects which may be generated by the iterative process. If we choose for our minimum quality C to be above 0.6 as quoted as an approximate limit for lithography in [11] then this strict “worst-case” metric shows that for our simulations at δz˜228 μm and below, a consistent and usable image may be generated. This value equates to δz˜0.25×DOF for this system at z˜16.2 mm. This procedure can therefore result in a well defied continuous image which we have verified experimentally. A set of test exposures were performed to show our continuous pattern in the focal region. The hologram generated using N=19 (δz=228 μm) was used as this is close to the lowest computing effort for a viable result. The optical setup is shown in FIG. 6, showing a laser (LR), spatial filter/beam expansion (SF), beam splitter (BS), modulator (SLM) and substrate (S).

The hologram was implemented on an 8 μm sample pitch phase-only spatial light modulator (SLM “Pluto” from Holoeye Photonics AG) by re-sampling the simulated hologram. This device is illuminated by an on-axis expanded laser beam (Coherent “Cube” 405 nm 50 mW). The photoresist used was “BPRS200”. This layer was approximately 2 μm thick.

Two images of the pattern developed on a coated substrate are shown in FIG. 7, in which FIG. 7( a) illustrates photoresist pattern on a flat top surface and FIG. 7( b) illustrates photoresist pattern on a 45° sloped surface. Hologram used: N=19 (bz=228 μm). The arrows in the figure indicate areas at the edge of image constraints for separate planes.

Continuous lines of requisite shape can be seen on both at and tilted sections with only small line width variation noticeable at the edges of constraint areas on separate planes.

In conclusion we have shown that simple phase only holograms generated by an iterative method can be used to produce continuous patterns of dense lines suitable for microelectronics fabrication on grossly non-planar substrates. We have presented an example where 8 lines of pitch 24 μm have been patterned onto a slope which is more than four times deeper than the depth of focus of the optical system. This is beyond the capabilities of a conventional optical projection system with a similar resolution limit.

In one or more exemplary embodiments, the functions and configurations described may be implemented in hardware, software, firmware, or any combination thereof. If implemented in software, the functions can be stored on or transmitted over as one or more instructions or code on a computer-readable medium. Computer-readable media includes both computer storage media and communication media including any medium that facilitates transfer of a computer program from one place to another. A storage media may be any available media that can be accessed by a computer. By way of example such computer-readable media can comprise RAM, ROM, EEPROM, CD-ROM or other optical disk storage, magnetic disk storage or other magnetic storage devices, or any other medium that can be used to carry or store desired program code in the form of instructions or data structures and that can be accessed by a computer. Also, any connection is properly termed a computer-readable medium. For example, if the software is transmitted from a website, server, or other remote source using a coaxial cable, fiber optic cable, twisted pair, digital subscriber line (DSL), or wireless technologies such as infrared, radio, and microwave, then the coaxial cable, fiber optic cable, twisted pair, DSL, or wireless technologies such as infrared, radio, and microwave are included in the definition of medium. Disk and disc, as used herein, includes compact disc (CD), laser disc, optical disc, digital versatile disc (DVD), floppy disk and blu-ray disc where disks usually reproduce data magnetically, while discs reproduce data optically with lasers. Combinations of the above should also be included within the scope of computer-readable media. The instructions or code associated with a computer-readable medium of the computer program product may be executed by a computer, e.g., by one or more processors, such as one or more digital signal processors (DSPs), general purpose microprocessors, ASICs, FPGAs, or other equivalent integrated or discrete logic circuitry.

Various improvements and modifications can be made to the above without departing from the scope of the invention.

References

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[6] R. Dorche, A. Lohmann, and Sinzinger, “Fresnel ping-pong algorithm for two-plane computer-generated hologram display,” Applied Optics 33, 869-875 (1994).

[7] J. Xia and H. Yin, “Three-dimensional light modulation using phase-only spatial light modulator,” Optical Engineering 48 (2009).

[8] M. Makowski, M. Sypek, A. Kolodziejczyk, and M. Grzegorz, “Three-plane phase-only computer hologram generated with iterative Fresnel algorithm,” Optical Engineering 44 (2005).

[9] J. Goodman, Introduction to Fourier Optics (Roberts and Company, 2005), 3rd ed.

[10] S. Maciej, “Light propogation in the Fresnel region. New numerical approach,” J. Optical Communications 116, 43-48 (1995).

[11] A. Wong, Resolution Enhancement Techniques in Optical Lithography, vol. TT47 of Tutorial Texts in Optical Engineering (SPIE Press, 2001).

[12] “W02006021818 ‘Holographic Lithography’

[13] G. e. a. Sinclair, “Interactive application in holographic optical tweezers of a multi-plane Gerchberg-Saxton algorithm for three-dimensional light shaping,” Optics Express 12, 1665-1670 (2004).

[14] A. Purvis, R. P. McWillliam, S. Johnson, N. Seed, G. Williams, M. A. and I. P. A., “Photolithographic patterning of bi-helical tracks onto conical substrates,” J. Micro/Nanolithography, MEMS and MOEMS 6 (2007). 

1. A method of generating a wave-optical exposure mask comprising: modifying the exposure mask via an iterative process until a modulation pattern produced by the exposure mask produces a desired non-planar pattern in object space; wherein said iterative process comprises specifying an intensity pattern that is defined over a bounded three dimensional geometrical surface by a series of multiple planes provided at differing positions within an image volume, extending from a diffraction plane formed by the modulation; and said iterative process is confined to a defined discrete array of amplitude and/or phase altering elements.
 2. The method of claim 1, wherein said iterative process includes: a long propagation from a diffraction plane to a first endpoint of the object space where the pattern is to be produced; one or more short propagations traversing the object space while applying different amplitude constraints across successive planes; a second long propagation from a second endpoint of the object space where the pattern is to be produced back to the diffraction plane; and the application of a phase-only constraint in the diffraction plane.
 3. The method of claim 2, wherein the iterative process further includes filtering and spatial constraints applied at the diffraction plane.
 4. The method of claim 1, wherein amplitude correction is applied to only a sub-portion of each image plane where the sampled pixels intersect a pseudo-continuous surface function.
 5. The method of claim 1, wherein amplitude and phase information is unconstrained in unimportant selected areas of an image volume such as to allow the convergence of the algorithm.
 6. The method of claim 1, wherein a propagation routine adopted to move between image planes and hologram is that of a convolution form of the Fresnel diffraction integral.
 7. The method of claim 1, wherein said propagation routine is an application of a Rayleigh-Somerfield propagator.
 8. The method of claim 1, wherein said propagation routine is an angular spectrum method.
 9. The method of claim 1, wherein each image plane is corrected with an ideal amplitude profile, whilst retaining the propagated phase.
 10. The method of claim 1, wherein the hologram plane itself is corrected with unit amplitude to give a phase only pattern.
 11. A wave-optical method of generating a hologram comprising: providing coherent or partially coherent radiation; modulating said incident radiation according to a modulation pattern; and varying said modulation pattern via an iterative process until said modulation pattern produces a desired non-planar pattern in object space; wherein said iterative process comprises specifying an intensity pattern that is defined over a bounded three dimensional geometrical surface by a series of multiple planes provided at differing positions within an image volume, extending from a diffraction plane formed by the modulation; and said iterative process is confined to a defined discrete array of amplitude and/or phase altering elements.
 12. The method of claim 11, further including the steps of claim
 1. 13. An apparatus for generating a hologram having a desired non-planar pattern in object space, comprising: a radiation source for emitting coherent or partially coherent radiation; a modulator for modulating said incident radiation according to a modulation pattern; said modulator being controllable to vary a pattern of modulation that is applied; said apparatus comprising a controller adapted to vary said modulation pattern via an iterative process until said modulation pattern produces a desired non-planar pattern in object space; wherein said iterative process comprises specifying an intensity pattern that is defined over a bounded three dimensional geometrical surface by a series of multiple planes provided at differing positions within an image volume, extending from a diffraction plane formed by the modulation; and said iterative process is confined to a defined discrete array of amplitude and/or phase altering elements.
 14. The apparatus of claim 13, wherein said modulator comprises a spatial light modulator (SLM).
 15. The apparatus of claim 13, wherein said radiation source comprises a laser.
 16. A lithographic apparatus comprising the apparatus of claim 13 and arranged for carrying out the method of claim
 1. 17. A consumer device for generating holograms comprising the apparatus of claim 13 and arranged for carrying out a method of generating a wave-optical exposure mask, the method comprising: modifying the exposure mask via an iterative process until a modulation pattern produced by the exposure mask produces a desired non-planar pattern in object space; wherein said iterative process comprises specifying an intensity pattern that is defined over a bounded three dimensional geometrical surface by a series of multiple planes provided at differing positions within an image volume, extending from a diffraction plane formed by the modulation; and said iterative process is confined to a defined discrete array of amplitude and/or phase altering elements.
 18. The consumer device of claim 17, comprising a holographic television with suitable projection means for projecting a hologram according to said predefined pattern into a viewing space or a display to be viewed by a user.
 19. A computer program product including instructions that, when run on an computer, enables said computer to implement a method of generating a wave-optical exposure mask, the method comprising: modifying the exposure mask via an iterative process until a modulation pattern produced by the exposure mask produces a desired non-planar pattern in object space; wherein said iterative process comprises specifying an intensity pattern that is defined over a bounded three dimensional geometrical surface by a series of multiple planes provided at differing positions within an image volume, extending from a diffraction plane formed by the modulation; and said iterative process is confined to a defined discrete array of amplitude and/or phase altering elements. 